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Math Help - Area of a Circular Segment

  1. #1
    ATC
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    Area of a Circular Segment

    While working on a problem, I had to look up a formula for the area of a circle segment. I have noticed that there is some ambiguity in the results.
    According to Wolfram Alpha, the formula is:
    Area of a Circular Segment-wolframalpha-20100823153307809.gif

    According to two other sources, the formula is:
    r^2(θ pi/180)

    Wolfram Alpha has been very reliable in the past, however I would prefer to not get this wrong due to a formula error. Please clarify which or what is correct. Thanks.
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  2. #2
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    Quote Originally Posted by ATC View Post
    While working on a problem, I had to look up a formula for the area of a circle segment. I have noticed that there is some ambiguity in the results.
    According to Wolfram Alpha, the formula is:
    Click image for larger version. 

Name:	wolframalpha-20100823153307809.gif 
Views:	19 
Size:	5.7 KB 
ID:	18691

    This is correct for angles expressed in radians.
    The triangle from the centre of the circle to the 2 points on the circumference
    is subtracted from the sector to obtain the segment.


    According to two other sources, the formula is:
    r^2(θ pi/180)

    This is the area of the sector for the angle expressed in degrees.
    The formula is converting degrees to radians and calculating the sector area.
    The triangle still needs to be subtracted to obtain the segment area.


    Wolfram Alpha has been very reliable in the past, however I would prefer to not get this wrong due to a formula error. Please clarify which or what is correct. Thanks.
    One formula calculates segment area, the second one calculates sector area.
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  3. #3
    MHF Contributor

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    You can learn the difference in circular segment and circular sector.
    Circular Segment -- from Wolfram MathWorld

    Circular Sector -- from Wolfram MathWorld
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